Skip to main content
SpringerLink
Log in

Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition

  • Theoretical advances
  • Published:
Pattern Analysis and Applications Aims and scope Submit manuscript

Abstract

Orthogonal moments have become a powerful tool for object representation and image analysis. Radial harmonic Fourier moments (RHFMs) are one of such image descriptors based on a set of orthogonal projection bases, which outperform other moments because of their computational efficiency. However, the conventional computational framework of RHFMs produces geometric error and numerical integration error, which will affect the accuracy of RHFMs, thus degrading the image reconstruction performance. To overcome this shortcoming, we propose a new computational framework of RHFMs, namely accurate quaternion radial harmonic Fourier moments (AQRHFMs), for color image processing, and also analyze the properties of AQRHFMs. Firstly, we propose a precise computation method of RHFMs to reduce the geometric and numerical errors. Secondly, by using the algebra of quaternions, we extend the accurate RHFMs to AQRHFMs in order to deal with the color images in a holistic manner. Experimental results show the proposed AQRHFMs achieve promising performance in image reconstruction and object recognition in both noise-free and noisy conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Xiao B, Wang G (2013) Generic radial orthogonal moment invariant for invariant image recognition. J Vis Commun Image Represent 24(7):1002–1008

    Article  Google Scholar 

  2. Wang C, Wang X, Li Y, Xia Z, Zhang C (2018) Quaternion polar harmonic Fourier moments for color images. Inf Sci 450:141–156

    Article  MathSciNet  Google Scholar 

  3. Khotanzad A, Hong Y (1990) Invariant image recognition by Zernike moments. IEEE Trans Pattern Anal Mach Intell 12(5):489–497

    Article  Google Scholar 

  4. Chong C, Raveendran P, Mukundan R (2004) Translation and scale invariants of Legendre moments. Pattern Recognit 37(1):119–129

    Article  Google Scholar 

  5. Gishkori S, Mulgrew B (2018) Pseudo-Zernike moments based sparse representations for SAR image classification. IEEE Trans Aerosp Electron Syst 55(2):1037–1044

    Article  Google Scholar 

  6. Zhi R, Cao L, Cao G (2018) Translation and scale invariants of Krawtchouk moments. Inf Process Lett 130:30–35

    Article  MathSciNet  Google Scholar 

  7. Ping Z, Wu R, Sheng Y (2002) Image description with Chebyshev–Fourier moments. J Opt Soc Am A 19(9):1748–1754

    Article  MathSciNet  Google Scholar 

  8. Xiao B, Ma J, Wang X (2010) Image analysis by Bessel–Fourier moments. Pattern Recognit 43(8):2620–2629

    Article  Google Scholar 

  9. Sheng YL, Shen LX (1994) Orthogonal Fourier–Mellin moments for invariant pattern recognition. J Opt Soc Am A 11(6):1748–1757

    Article  Google Scholar 

  10. Hu H, Zhang Y, Shao C, Ju Q (2014) Orthogonal moments based on exponent functions: exponent Fourier moments. Pattern Recognit 47(8):2596–2606

    Article  Google Scholar 

  11. Upneja R, Pawlak M, Sahan A (2018) An accurate approach for the computation of polar harmonic transforms. Optik 158:623–633

    Article  Google Scholar 

  12. Ren H, Ping Z, Bo W, Wu W, Sheng Y (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A 20(4):631–637

    Article  MathSciNet  Google Scholar 

  13. Wang C, Wang X, Xia Z, Zhang C (2019) Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Inf Sci 470:109–120

    Article  Google Scholar 

  14. Singh C, Upneja R (2012) A computational model for enhanced accuracy of radial harmonic Fourier moments. In: World congress of engineering, London, UK, pp 1189–1194

  15. Singh C, Ranade S (2013) A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments. Dig Signal Process 23(5):1470–1482

    Article  MathSciNet  Google Scholar 

  16. Wang C, Wang X, Xia Z (2016) Geometrically invariant image watermarking based on fast radial harmonic Fourier moments. Signal Process Image Commun 45:10–23

    Article  Google Scholar 

  17. Deng A, Wei C, Gwo C (2016) Stable, fast computation of high-order Zernike moments using a recursive method. Pattern Recognit 56:16–25

    Article  Google Scholar 

  18. Upneja R (2016) Accurate and fast Jacobi–Fourier moments for invariant image recognition. Optik 127(19):7925–7940

    Article  Google Scholar 

  19. Li C, Li Y, Yuan Y, Wu X, Sang Q (2018) Quaternion wavelet transform based full reference image quality assessment for multiply distorted images. PLoS ONE 13(6):e0199430

    Article  Google Scholar 

  20. Liu F, Ma L, Liu C, Lu Z (2018) Optimal blind watermarking for color images based on the U matrix of quaternion singular value decomposition. Multimed Tools Appl 77(18):23483–23500

    Article  Google Scholar 

  21. Wang C, Wang X, Zhang C, Xia Z (2017) Geometric correction based color image watermarking using fuzzy least squares support vector machine and Bessel K form distribution. Signal Process 134:197–208

    Article  Google Scholar 

  22. Xia Z, Wang X, Zhou W, Li R, Wang C, Zhang C (2019) Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process 157:108–118

    Article  Google Scholar 

  23. Guo L, Zhu M (2011) Quaternion Fourier–Mellin moments for color images. Pattern Recognit 44(2):187–195

    Article  Google Scholar 

  24. Chen B, Shu H, Zhang H, Chen G, Tounoulin C, Dillenseger JL, Luo LM (2012) Quaternion Zernike moments and their invariant for color image analysis and object recognition. Signal Process 92(2):308–318

    Article  Google Scholar 

  25. Guo LQ, Dai M, Zhu M (2014) Quaternion moment and its invariant for color object classification. Inf Sci 273:132–143

    Article  MathSciNet  Google Scholar 

  26. Shao Z, Shu H, Wu J, Chen B, Coatrieux J (2014) Quaternion Bessel–Fourier moments and their invariant descriptors for object reconstruction and recognition. Pattern Recognit 47(2):603–611

    Article  Google Scholar 

  27. Chen B, Shu H, Coatrieux G, Chen G, Sun X, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124–144

    Article  MathSciNet  Google Scholar 

  28. Wang C, Wang X, Xia Z, Zhang C, Chen X (2016) Geometrically resilient color image zero-watermarking algorithm based on quaternion exponent moments. J Vis Commun Image Represent 41:247–259

    Article  Google Scholar 

  29. Wang X, Liu Y, Xu H, Wang P, Yang H (2018) Robust copy–move forgery detection using quaternion exponent moments. Pattern Anal Appl 21(2):451–467

    Article  MathSciNet  Google Scholar 

  30. Wang X, Li W, Yang H, Niu P, Li Y (2015) Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt Laser Technol 66:78–88

    Article  Google Scholar 

  31. Xia Z, Wang X, Li X, Wang M, Zhao T (2019) Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Process 164:368–379

    Article  Google Scholar 

  32. Yang T, Ma J, Miao Y, Wang X, Xiao B, He B, Meng Q (2019) Quaternion weighted spherical Bessel–Fourier moment and its invariant for color image reconstruction and object recognition. Inf Sci 505:388–405

    Article  MathSciNet  Google Scholar 

  33. Hosny K, Darwish M (2019) Invariant color images representation using accurate quaternion Legendre–Fourier moments. Pattern Anal Appl 22(3):1105–1122

    Article  MathSciNet  Google Scholar 

  34. https://www.cs.columbia.edu/CAVE/software/softlib/coil-100.php

  35. Xiao B, Ma JF, Wang X (2010) Image analysis by Bessel–Fourier moments. Pattern Recognit 43(8):2060–2629

    Article  Google Scholar 

  36. Xiao B, Wang G (2013) Generic radial orthogonal moment invariants for invariant image recognition. J Vis Commun Image Represent 24(7):1002–1008

    Article  Google Scholar 

  37. https://cswww.essex.ac.uk/mv/allfaces/index.html

Download references

Acknowledgments

This work was partially supported by the National Science Fund of China under Grant Nos. 61702262, 61861136011, and U1713208; Program for Changjiang Scholars; Natural Science Foundation of Jiangsu Province under Grant No. BK20181299; CCF-Tencent Open Fund (RAGR20180113); Young Elite Scientists Sponsorship Program by GAST (2018QNRC001); Science and Technology on Parallel and Distributed Processing Laboratory (PDL) Open Fund (WDZC20195500106); Fundamental Research Funds for the Central Universities under Grant No. 30918011322.

Author information

Authors and Affiliations

  1. PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, and Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Yunan Liu, Shanshan Zhang & Jian Yang

  2. National Ocean Technology Center, Tianjin, 300112, People’s Republic of China

    Houjun Wang

Authors
  1. Yunan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shanshan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guangyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Houjun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shanshan Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Zhang, S., Li, G. et al. Accurate quaternion radial harmonic Fourier moments for color image reconstruction and object recognition. Pattern Anal Applic 23, 1551–1567 (2020). https://doi.org/10.1007/s10044-020-00877-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10044-020-00877-6

Keywords

Search

Navigation